The solution of linear flutter equations carries the risk of missing important aeroelastic modes, particularly with large, complex models or control systems. A mathematical technique known as the topological degree of a system of nonlinear equations tells how many roots the equations have within a given region. Using the degree to determine the number of roots of the flutter determinant, regions, such as a velocity–frequency interval, can be tested for missed neutral-stability points. A generalized-bisection technique, together with the topological degree, provides a globally convergent nonlinear-equation solver requiring only function values. Applied to flutter equations, it is a safe way to narrow regions containing neutral-stability points or start points for aeroelastic mode-tracking processes in preparation for more efficient techniques, such as Newton’s method.
Topological Degree Applied to Flutter Equations
AIAA Journal ; 53 , 3 ; 763-770
2014-12-01
8 pages
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
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